1.已知:x+y=0.2,x+3y=1,求3x^2+12xy+12y^2的值.2.化简:(1) (x^2-6x+9)/(x^2-4)(2) (x^2-4x)/(x^2-8x+16)3.解方程:(1) 1/(x-4)=4/(x^2-16)(2) 3/(x-1)-(x+2)/[x(x-1)]=0(3) (2-x)/(x-3)+1/(3-x)=1如果过程写得好,
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1.已知:x+y=0.2,x+3y=1,求3x^2+12xy+12y^2的值.
2.化简:
(1) (x^2-6x+9)/(x^2-4)
(2) (x^2-4x)/(x^2-8x+16)
3.解方程:
(1) 1/(x-4)=4/(x^2-16)
(2) 3/(x-1)-(x+2)/[x(x-1)]=0
(3) (2-x)/(x-3)+1/(3-x)=1
如果过程写得好,
x+y=0.2,x+3y=1
相加
2x+4y=1.2
x+2y=0.6
3x^2+12xy+12y^2
=3(x^2+4xy+4y^2)
=3(x+2y)^2
=3*0.6^2
=1.08
(1) (x^2-6x+9)/(x^2-4)
=(x-3)^2/(x-2)(x+2)
写错了,如果是(x^2-6x+9)/(x^2-9)则
=(x-3)^2/(x+3)(x-3)
=(x-3)/(x+3)
(2) (x^2-4x)/(x^2-8x+16)
=x(x-4)/(x-4)^2
=x/(x-4)
(1) 1/(x-4)=4/(x^2-16)
1/(x-4)=4/(x+4)(x-4)
两边乘(x+4)(x-4)
x+4=4
x=0
经检验,x=0是方程的解
(2) 3/(x-1)-(x+2)/[x(x-1)]=0
两边乘x(x-1)
3x-(x+2)=0
2x-2=0
x=1
经检验,x=1使公分母x(x-1)=0,是增根,舍去
所以方程无解
(3) (2-x)/(x-3)+1/(3-x)=1
(2-x)/(x-3)-1/(x-3)=1
两边乘x-3
2-x-1=x-3
2x=4
x=2
经检验,x=2是方程的解
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